Some Extinction Effects in Insulating Spheres

In the preceding section and elsewhere we have touched on a few points that deserve further elaboration. For example, we have emphasized that extinction calculations should, in general, be done with wavelength-dependent optical 

Extinction features that strongly depend on particle size will be obscured, if not totally obliterated, in a polydispersion. Many analytical expressions for the radius probability distribution have been used in Mie calculations. For purposes of illustration we have chosen the Gaussian distribution, according to which the probability that a sphere has radius between a and a + da is 

To show the effect of increasing size dispersion on extinction,a series of calculations for water droplets is given in Fig. 11.6. The topmost curve reproduces the calculations of Fig. 11.5a for a single sphere the standard deviation a is increased in successively lower curves. 

Ripple structure, beginning with the sharpest at large size parameters, is the first to disappear as a is increased. As the distribution is further widened, the interference structure fades away. For the widest distribution the only remaining features are reddening at small size parameters, and, at the other extreme, an asymptotic approach to the limiting value 2. if ( K / 

Without an appreciation for the possible spread of sizes in real particulate systems the values of a in Fig. 11.6 are merely those of an adjustable parameter. We therefore give distribution widths for some natural and artificial aerosols and hydrosols in Table 11.1 we excluded from this list broad distributions, such as raindrops, to which the notion of a width is not really applicable. 

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